You, my good friend, have just hit the nail on the head. Yes, you should focus on the unconditional, non-toxic love that you can give yourself but also on forgiving the past hurts and experiences inflicted upon you by your parents.
People cheat because they cannot be honest with others, let alone themselves. And if you cannot truly be honest with yourself there is definitely no way that you can truly love yourself. And if you cannot love yourself, you cannot love anyone else. And people who cheat just do not have enough self-love to own their truths.